Construction in GCLC language
dim 120 120
point E_{c} 95 56.36
point M_{a} 65 40
point M_{b} 95 67.5
color 220 0 0
fontsize 11
cmark_r E_{c}
cmark_b M_{a}
cmark_rt M_{b}
color 0 0 0
fontsize 10
% DET: points E_{c} and M_{a} are not the same
% Constructing bisector m(E_{c}M_{a}) of the segment E_{c}M_{a}
med m(E_{c}M_{a}) E_{c} M_{a}
color 200 200 200
drawline m(E_{c}M_{a})
color 0 0 0
color 200 200 200
drawsegment E_{c} M_{a}
color 0 0 0
% DET: points E_{c} and M_{b} are not the same
% Constructing bisector m(E_{c}M_{b}) of the segment E_{c}M_{b}
med m(E_{c}M_{b}) E_{c} M_{b}
color 200 200 200
drawline m(E_{c}M_{b})
color 0 0 0
color 200 200 200
drawsegment E_{c} M_{b}
color 0 0 0
% NDG: lines m(E_{c}M_{b}) and m(E_{c}M_{a}) are not parallel% DET: lines m(E_{c}M_{b}) and m(E_{c}M_{a}) are not the same
% Constructing a point N which belongs to line m(E_{c}M_{b}) and line m(E_{c}M_{a})
intersec N m(E_{c}M_{b}) m(E_{c}M_{a})
cmark_r N
% DET: points M_{a} and N are not the same
% Constructing a line m(H_{b}H_{c}) which passes through point M_{a} and point N
line m(H_{b}H_{c}) M_{a} N
color 200 200 200
drawline m(H_{b}H_{c})
color 0 0 0
% NDG: points E_{c} and N are not the same
% Constructing a circle k(N,M_{a}) whose center is at point N and which passes through point E_{c}
circle k(N,M_{a}) N E_{c}
color 200 200 200
drawcircle k(N,M_{a})
color 0 0 0
% NDG: line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect% DET: points M_{a} and E_{a} must be different
% Constructing a point E_{a} which is an image of the point M_{a} in the symmetry to point/line N
sim E_{a} N M_{a}
cmark_r E_{a}
% DET: points M_{b} and E_{a} are not the same
% Constructing a line m(AH_{c}) which passes through point M_{b} and point E_{a}
line m(AH_{c}) M_{b} E_{a}
color 200 200 200
drawline m(AH_{c})
color 0 0 0
% Constructing a line h_{c} which contains the point E_{c} and is parallel to the line m(AH_{c})
parallel h_{c} E_{c} m(AH_{c})
color 200 200 200
drawline h_{c}
color 0 0 0
% NDG: line h_{c} and circle k(N,M_{a}) intersect% DET: points E_{c} and H_{c} must be different
% Constructing a point P_{\_G58449} which is a foot of the point N on the line h_{c}
foot P_{\_G58449} N h_{c}
cmark_r P_{\_G58449}
color 200 200 200
drawline N P_{\_G58449}
color 0 0 0
% Constructing a point H_{c} which is an image of the point E_{c} in the symmetry to point/line P_{\_G58449}
sim H_{c} P_{\_G58449} E_{c}
cmark_lt H_{c}
% NDG: points H_{c} and M_{a} are not the same
% Constructing a circle k(M_{a},B) whose center is at point M_{a} and which passes through point H_{c}
circle k(M_{a},B) M_{a} H_{c}
color 200 200 200
drawcircle k(M_{a},B)
color 0 0 0
% NDG: line h_{c} and circle k(M_{a},B) intersect% DET: points H_{c} and C must be different
% Constructing a point P_{\_G58753} which is a foot of the point M_{a} on the line h_{c}
foot P_{\_G58753} M_{a} h_{c}
cmark_r P_{\_G58753}
color 200 200 200
drawline M_{a} P_{\_G58753}
color 0 0 0
% Constructing a point C which is an image of the point H_{c} in the symmetry to point/line P_{\_G58753}
sim C P_{\_G58753} H_{c}
cmark_b C
% Constructing a point B such that M_{a}B/M_{a}C=-1
towards B M_{a} C -1
cmark_b B
color 200 200 200
drawsegment C B
color 0 0 0
% Constructing a point A such that M_{b}A/M_{b}C=-1
towards A M_{b} C -1
cmark_t A
color 200 200 200
drawsegment C A
color 0 0 0
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: line h_{c} and circle k(M_{a},B) intersect; points H_{c} and M_{a} are not the same; line h_{c} and circle k(N,M_{a}) intersect; line m(H_{b}H_{c}) and circle k(N,M_{a}) intersect; points E_{c} and N are not the same; lines m(E_{c}M_{b}) and m(E_{c}M_{a}) are not parallel
% Determination conditions: points H_{c} and C must be different; points E_{c} and H_{c} must be different; points M_{b} and E_{a} are not the same; points M_{a} and E_{a} must be different; points M_{a} and N are not the same; lines m(E_{c}M_{b}) and m(E_{c}M_{a}) are not the same; points E_{c} and M_{b} are not the same; points E_{c} and M_{a} are not the same